Searches for a YouTube link cleaner, a YouTube link sanitizer, a YouTube tracking link remover, or simply how to remove tracking from a YouTube link all describe one operation: deleting the query parameters that identify you or the surface you shared from, while leaving the ones that identify the video and the position in it. This page does that operation.
You do not need an extension for it. The cleaning runs as JavaScript on this page, against rules that ship with the page, so there is no request to a server carrying your link and nothing to install. If you would rather see every rule that exists rather than just the YouTube ones, the main URL Cleaner lists them all.